1. Field of the Invention
The present invention relates to optical instruments and methods for aiming a rifle, external ballistics and methods for predicting a gyroscopically stabilized projectile's trajectory to a target. This application relates to projectile weapon aiming systems such as rifle scopes, to reticle configurations for projectile weapon aiming systems, and to associated methods of compensating for a projectile's external ballistic behavior while developing a field expedient firing solution.
2. Discussion of the Prior Art
Rifle marksmanship has been continuously developing over the last few hundred years, and now refinements in materials and manufacturing processes have made increasingly accurate aimed fire possible. These refinements have made previously ignored environmental and external ballistics factors more significant as sources of aiming error.
The term “rifle” as used here, means a projectile controlling instrument or weapon configured to aim and propel or shoot a projectile, and rifle sights or projectile weapon aiming systems are discussed principally with reference to their use on rifles and embodied in telescopic sights commonly known as rifle scopes. It will become apparent, however, that projectile weapon aiming systems may include aiming devices other than rifle scopes, and may be used on instruments or weapons other than rifles which are capable of controlling and propelling projectiles along substantially pre-determinable trajectories (e.g., rail guns or cannon). The prior art provides a richly detailed library documenting the process of improving the accuracy of aimed fire from rifles (e.g., as shown in FIG. 1A) and other firearms or projectile weapons.
Most shooters or marksmen, whether hunting or target shooting, understand the basic process for aiming. The primary aiming factors are (a) elevation, for range or distance to the target or Point of Aim (“POA”), where the selected elevation determines the arcuate trajectory and “drop” of the bullet in flight and the Time of Flight (“TOF”), and (b) windage, because transverse or lateral forces act on the bullet during TOF and cause wind deflection or lateral drift. All experienced marksmen account for these two factors when aiming. Precision long-range shooters such as military and police marksmen (or “snipers”) often resort to references including military and governmental technical publications such as the following:                (Ref 1) Jonathan M. Weaver, Jr., LTC, USA Ret., Infantry, System Error Budgets, Target Distributions and Hitting Performance Estimates for General-Purpose Rifles and Sniper Rifles of 7.62×51 mm and Larger Calibers, AD-A228 398, TR-461, AMSAA, May, 1990;        (Ref 2) McCoy, Robert L., A Parametric Study of the Long Range, Special Application Sniper Rifle, Aberdeen Proving Grounds (“APG”), MD, BRL Memorandum Report No. 3558, December 1986;        (Ref 3) Brophy, William S., Maj., Ord., A Test of Sniper Rifles, 37th Report of Project No. TS2-2015, APG, MD D&PS, 27 July 1955;        (Ref 4) Von Wahlde, Raymond & Metz, Dennis, Sniper Weapon Fire Control Error Budget Analysis, US Army ARL-TR-2065, August, 1999—arl.army.mil;        (Ref 5) US Army FM-23-10, Sniper Training, United States Army Infantry School ATSH-IN-S3, Fort Benning, Ga. 31905-5596, August 1994; and        (Ref 6) USMC MCWP 3-15,3 (formerly FMFM 1-3B), Sniping, PCN 143 000118 00, Doctrine Division (C42) US Marine Corps Combat Development Command, 2 Broadway Street Suite 210 Quantico, Va. 22134-5021, May 2004.For nomenclature purposes and to provide a more complete background and foundation for what follows, these published references are incorporated herein by reference.        
A number of patented rifle sights or projectile weapon aiming systems have been developed to help marksmen account for the elevation/range and windage factors when aiming. For example, U.S. Pat. No. 7,603,804 (to Zadery et al) describes a riflescope made and sold by Leupold & Stevens, Inc., with a reticle including a central crosshair defined as the primary aiming mark for a first selected range (or “zero range”) and further includes a plurality of secondary aiming marks spaced below the primary aiming mark on a primary vertical axis. Zadery's secondary aiming marks are positioned to compensate for predicted ballistic drop at selected incremental ranges beyond the first selected range, for identified groups of bullets having similar ballistic characteristics.
Zadery's rifle scope has variable magnification, and since Zadery's reticle is not in the first focal plane (“F1”) the angles subtended by the secondary aiming marks of the reticle can be increased or decreased by changing the optical power of the riflescope to compensate for ballistic characteristics of different ammunition. The rifle scope's crosshair is defined by the primary vertical line or axis which is intersected by a perpendicular horizontal line or primary horizontal axis. The reticle includes horizontally projecting windage aiming marks on secondary horizontal axes intersecting selected secondary aiming marks, to facilitate compensation for the effect of crosswinds on the trajectory of the projectile at the selected incremental ranges At each secondary aiming mark on the primary vertical axis, the laterally or horizontally projecting windage aiming marks project symmetrically (left and right) from the vertical axis, indicating a windage correction for wind from the shooter's right and left sides, respectively.
Beyond bullet drop over a given range and basic left-right or lateral force windage compensation, there are several other ballistic factors which result in lesser errors in aiming. As the inherent precision of rifles and ammunition improves, it is increasingly critical that these other factors be taken into consideration and compensated for, in order to make an extremely accurate shot. These factors are especially critical at very long ranges, (e.g., approaching or beyond one thousand yards). Many of these other factors were addressed in this applicant's U.S. Pat. No. 7,325,353 (to Cole & Tubb) which describes a riflescope reticle including a plurality of charts, graphs or nomographs arrayed so a shooter can solve the ranging and ballistic problems required for correct estimation and aiming at a selected target. The '353 patent's scope reticle includes at least one aiming point field to allow a shooter to compensate for range (with elevation) and windage, with the “vertical” axis precisely diverging to compensate for “spin drift” and precession at longer ranges. Stadia for determining angular target dimension(s) are included on the reticle, with a nomograph for determining apparent distance from the apparent dimensions being provided either on the reticle or external to the scope. Additional nomographs are provided for the determination and compensation of non-level slopes, non-standard density altitudes, and wind correction, either on the reticle or external to the riflescope.
The elevation and windage aim point field (50) in the '353 patent's reticle is comparable, in one respect, to traditional bullet drop compensation reticles such as the reticle illustrated in the Zaderey '804 patent, but includes a number of refinements such as the compensated elevation or “vertical” crosshair 54, which can be seen to diverge laterally away from a true vertical reference line 56 (e.g., as shown in FIG. 3 of the '353 patent), to the right (i.e., for a rifle barrel with rifling oriented for right hand twist). The commercial embodiment of the '353 patent reticle is known as the DTAC™ Reticle, and the RET-2 version of the DTAC reticle is illustrated in FIG. 1C.
The compensated elevation or “vertical” crosshair of the DTAC™ reticle is useful for estimating the ballistic effect of the bullet's gyroscopic precession or “spin drift” caused by the bullet's stabilizing axial rotation or spin, which is imparted on the bullet by the rifle barrel's inwardly projecting helical “lands” which bear upon the bullet's circumferential surfaces as the bullets accelerates distally down the barrel. Precession or “spin drift” is due to an angular change of the axis of the bullet in flight as it travels an arcuate ballistic flight path. While various corrections have been developed for most of these factors, the corrections were typically provided in the form of programmable electronic devices or earlier in the form of logbooks developed over time by precision shooters. Additional factors affecting exterior ballistics of a bullet in flight include atmospheric variables, specifically altitude and barometric pressure, temperature, and humidity.
Traditional telescopic firearm sight reticles have been developed with markings to assist the shooter in determining the apparent range of a target. A nearly universal system has been developed by the military for artillery purposes, known as the “mil-radian,” or “mil,” for short. This system has been adopted by most of the military for tactical (e.g., sniper) use, and was subsequently adopted by most of the sport shooting world. The mil is an angle having a tangent of 0.001. A mil-dot scale is typically an array of dots (or similar indicia) arrayed along a line which is used to estimate or measure the distance to a target by observing the apparent target height or span (or the height or span of a known object in the vicinity of the target). For example, a target distance of one thousand yards would result in one mil subtending a height of approximately one yard, or thirty six inches, at the target. This is about 0.058 degree, or about 3.5 minutes of angle. It should be noted that although the term “mil-radian” implies a relationship to the radian, the mil is not exactly equal to an angle of one one thousandth of a radian, which would be about 0.057 degree or about 3.42 minutes of angle. The “mil-dot” system, based upon the mil, is in wide use in scope reticle marking, but does not provide a direct measure for determining the distance to a target without first having at least a general idea of the target size, and then performing a mathematical calculation involving these factors. Confusingly, the US Army and the US Marine Corps do not agree on these conversions exactly (see, e.g., Refs 5 and 6), which means that depending on how the shooter is equipped, the shooter's calculations using these conversions may change slightly.
The angular measurement known as the “minute of angle,” or MOA is used to measure the height or distance subtended by an angle of one minute, or one sixtieth of one degree. At a range of one hundred yards, this subtended angle spans slightly less than 1.05 inches, or about 10.47 inches at one thousand yards range. It will be seen that the distance subtended by the MOA is substantially less than that subtended by the mil at any given distance, i.e. thirty six inches for one mil at one thousand yards but only 10.47 inches for one MOA at that range. Thus, shooters have developed a rather elaborate set of procedures to calculate required changes to sights (often referred to as “clicks”) based on a required adjustment in a bullet's point of impact (e.g., as measured in “inches” or “minutes”).
Sight adjustment and ranging methods have been featured in a number of patents Assigned to Horus Vision, LLC, including U.S. Pat. Nos. 6,453,595 and 6,681,512, each entitled “Gunsight and Reticle therefore” by D. J. Sammut and, more recently, U.S. Pat. No. 7,832,137, entitled “Apparatus and Method for Calculating Aiming Point Information” by Sammut et al. These patents describe several embodiments of the Horus Vision™ reticles, which are used in conjunction with a series of calculations to provide predicted vertical corrections (or holdovers) for estimated ranges and lateral corrections (or windage adjustments), where a shooter calculates holdover and windage adjustments separately, and then selects a corresponding aiming point on the reticle.
In addition to the general knowledge of the field of the present invention described above, the applicant is also aware of certain foreign references which relate generally to the invention. Japanese Patent Publication No. 55-36,823 published on Mar. 14, 1980 to Raito Koki Seisakusho KK describes (according to the drawings and English abstract) a variable power rifle scope having a variable distance between two horizontally disposed reticle lines, depending upon the optical power selected. The distance may be adjusted to subtend a known span or dimension at the target, with the distance being displayed numerically on a circumferential external adjustment ring. A prism transmits the distance setting displayed on the external ring to the eyepiece of the scope, for viewing by the marksman.
General & Specialized Nomenclature
In order to provide a more structured background and a system of nomenclature, we refer again to FIGS. 1A-1F. FIG. 1A illustrates a projectile weapon system 4 including a rifle 6 and a telescopic rifle sight or projectile weapon aiming system 10. Telescopic rifle sight or rifle scope 10 are illustrated in the standard configuration where the rifle's barrel terminates distally in an open lumen or muzzle and rifle scope 10 is mounted upon rifle 6 in a configuration which allows the rifle system 4 to be “zeroed” or adjusted such that a user or shooter sees a Point of Aim (“POA”) in substantial alignment with the rifle's Center of Impact (“COI”) when shooting or firing a selected projectile 26 at a selected target 28.
FIG. 1B schematically illustrates exemplary internal components for telescopic rifle sight or rifle scope 10. The scope 10 generally includes a distal objective lens 12 opposing a proximal ocular or eyepiece lens 14 at the ends of a rigid and substantially tubular body or housing, with a reticle screen or glass 16 disposed there-between. Variable power (e.g., 5-15 magnification) scopes also include an erector lens 18 and an axially adjustable magnification power adjustment (or “zoom”) lens 20, with some means for adjusting the relative position of the zoom lens 20 to adjust the magnification power as desired, e.g. a circumferential adjustment ring 22 which threads the zoom lens 20 toward or away from the erector lens 18. Variable power scopes, as well as other types of telescopic sight devices, also often include a transverse position control 24 for transversely adjusting the reticle screen 16 to position an aiming point or center of the aim point field thereon (or adjusting the alignment of the scope 10 with the firearm 6), to adjust vertically for elevation (or bullet drop) as desired. Scopes also conventionally include a transverse windage adjustment for horizontal reticle screen control as well (not shown).
While an exemplary conventional variable power scope 10 is used in the illustrations, fixed power scopes (e.g., 10×, such as the M3A scope) are often used. Such fixed power scopes have the advantages of economy, simplicity, and durability, in that they eliminate at least one lens and a positional adjustment for that lens. Such a fixed power scope may be suitable for many marksmen who generally shoot at relatively consistent ranges and targets.
Variable power scopes include two focal planes. The reticle screen or glass 16 used in connection with the reticles of the present invention is preferably positioned at the first or front focal plane (“FP1”) between the distal objective lens 12 and erector lens 18, in order that the reticle thereon will change scale correspondingly with changes in magnification as the power of the scope is adjusted. This results in reticle divisions subtending the same apparent target size or angle, regardless of the magnification of the scope. In other words, a target subtending two reticle divisions at a relatively low magnification adjustment, will still subtend two reticle divisions when the power is adjusted, to a higher magnification, at a given distance from the target. The FP1 reticle location is often preferred by military and police marksmen using reticle systems with “mil-dot” divisions in variable power firearm scopes.
Alternatively, reticle screen 16 may be placed at a second or rear focal plane between the zoom lens 20 and proximal eyepiece 14, if so desired. Such a second focal plane reticle will remain at the same apparent size regardless of the magnification adjustment to the scope, which has the advantage of providing a full field of view to the reticle at all times. However, the reticle divisions will not consistently subtend the same apparent target size with changes in magnification, when the reticle is positioned at the second focal plane in a variable power scope.
FIG. 1C illustrates an earlier revision of applicant's DTAC™ rifle scope reticle, and provides a detailed view of an exemplary elevation and windage aim point field 30, with the accompanying horizontal and vertical angular measurement stadia 31. The aim point field 30 must be located on the scope reticle 16, as the marksman uses the aim point field 30 for aiming at the target as viewed through the scope and its reticle. Aim point field 30 comprises at least a horizontal line or crosshair 32 and a substantially vertical line or crosshair 34, which in the case of the field 30 is represented by a line of substantially vertical dots. A true vertical reference line (not shown) on aim point field 30 would vertical crosshair of the field 30, if so desired. It is noted that the substantially vertical central aiming dot line 34 is skewed somewhat to the right of a true vertical reference line (not shown) to compensate for gyroscopic precession or “spin drift” of the bullet in its trajectory. Most rifle barrels manufactured in the U.S. have “right hand twist” rifling which spirals to the right, or clockwise, from the proximal chamber to the distal muzzle of the rifle's barrel. This imparts a corresponding clockwise gyroscopically stabilizing spin to the fired bullet. As the fired bullet travels an arcuate trajectory in its ballistic flight between the rifle's muzzle and the target, the longitudinal axis of the bullet will deflect angularly to follow that arcuate trajectory. The spin of the bullet results in gyroscopic precession ninety degrees to the arcuate trajectory, causing the bullet to deflect to the right (for right hand twist barrels). This effect is seen most clearly at relatively long ranges, where there is substantial arc to the trajectory of the bullet, as shown in FIG. 1E. The offset or skewing of the vertical aiming dot line 34 to the right, in use, results in the marksman correspondingly moving the alignment slightly to the left in order to position one of the dots of the line 34 on the target (assuming no windage correction). This has the effect of correcting for the rightward deflection of the bullet due to gyroscopic precession.
The horizontal crosshair 32 and central aiming dot line 34 define a single aim point 38 at their intersection. The multiple aim point field 30 is formed of a series of horizontal rows which are seen in FIG. 1C to be exactly parallel to horizontal crosshair 32 and provide angled columns which are generally vertical (but spreading as they descend) to provide left side columns and right side columns of aiming dots (which may be small circles or other shapes, in order to minimize the obscuration of the target). It will be noted that the first and second uppermost horizontal rows actually comprise only a single dot each (including 38), as they provide relatively close-in aiming points for targets at only one hundred and two hundred yards, respectively. FIG. 1C's aim point field 30 is configured for a rifle and scope system which has initially been “zeroed” (i.e., adjusted to exactly compensate for the drop of the bullet during its flight) at a distance of two hundred yards, as evidenced by the primary horizontal crosshair 32. Thus, a marksman aiming at a closer target must lower his aim point to one of the dots slightly above the horizontal crosshair 32, as relatively little drop occurs to the bullet in such a relatively short flight.
Most of the horizontal rows in FIG. 1C's aim point field 30 are numbered along the left edge of the aim point field to indicate the range in hundreds of yards for an accurate shot using the dots of that particular row (e.g., “3” for 300 yards and “4” for 400 yards). The spacing between each horizontal row gradually increases as the range becomes longer and longer. This is due to the slowing of the bullet and increase in vertical speed due to the acceleration of gravity during the bullet's flight, (e.g., as illustrated in FIG. 1E). The alignment and spacing of the horizontal rows compensates for these factors at the selected ranges. In a similar manner, the angled, generally vertical columns spread as they extend downwardly to greater and greater ranges. These generally vertical columns are intended to provide aim points which compensate for windage, i.e. the lateral drift of a bullet due to any crosswind component. A crosswind will have an ever greater effect upon the path of a bullet with longer and longer range or distance. The scope reticle of FIG. 1C includes approximate “lead” indicators “W” (for a target moving at a slow, walking speed) and “R” (farther from the central aim point 38, for running targets).
In order to use the Tubb™ DTAC™ elevation and windage aim point field 30, the marksman must have a reasonably close estimate or measurement of the range to the target. This can be provided by means of the evenly spaced horizontal and vertical angular measurement stadia 31 disposed upon aim point field 30. The stadia 31 comprise a vertical row of stadia alignment markings and a horizontal row of such markings disposed along the horizontal reference line or crosshair 32. Each adjacent stadia mark, e.g. vertical marks and horizontal marks are evenly spaced from one another and subtend precisely the same angle therebetween, e.g. one mil, or a tangent of 0.001. Other angular definitions may be used as desired, e.g. the minute of angle or MOA system discussed above. The DTAC™ stadia system 31 is used by estimating some dimension of the target, or of an object close to the target. Each of the stadia markings comprises a small triangular shape, and provides a precise, specific alignment line, to reduce errors in subtended angle estimation, and therefore in estimating the distance to the target.
FIG. 1D illustrates a rifle scope reticle which is similar in many respects to the reticle of FIG. 10 and applicant's previous DTAC™ Reticle, as described and illustrated in applicant's own U.S. Pat. No. 7,325,353, in the prior art. FIG. 10 provides a detailed view of an exemplary elevation and windage aim point field 50, with the accompanying horizontal and vertical angular measurement stadia 100. The aim point field 50 must be located on the scope reticle 16, as the marksman uses the aim point field 50 for aiming at the target as viewed through the scope and its reticle. The aim point field 50 comprises at least one horizontal line or crosshair 52 and a substantially vertical central aiming dot line or crosshair 54, which in the case of the field 50 is represented by a line of substantially or nearly vertical dots. A true vertical reference line 56 is shown on the aim point field 50 of FIG. 1D, and may comprise the vertical crosshair of the reticle aim point field 50, if so desired.
It will be noted that the substantially vertical central aiming dot line 54 is skewed somewhat to the right of the true vertical reference line 56. As above, this is to compensate for gyroscopic precession or “spin drift” of a spin-stabilized bullet or projectile in its trajectory. The flying bullet's clockwise spin results in gyroscopic precession which generates a force that is transverse or normal (i.e., ninety degrees) to the arcuate trajectory, causing the bullet to deflect to the right. As above, the lateral offset or skewing of substantially vertical central aiming dot line to the right causes the user, shooter or marksman to aim or moving the alignment slightly to the left in order to position one of the aiming dots of the central line 54 on the target (assuming no windage correction).
FIG. 1D shows how horizontal crosshair 52 and substantially vertical central aiming dot line 54 define a single aim point 58 at their intersection. The multiple aim point 50 is formed of a series of horizontal rows which are exactly parallel to horizontal crosshair 52 (60a, 60b, 60c, etc.) and angled but generally vertical (spreading as they descend) to provide left side columns 62a, 62b, 62c, etc. and right side columns 64a, 64b, 64c, etc. of aiming dots (which may be small circles or other shapes, in order to minimize the obscuration of the target). It will be noted that the two uppermost horizontal rows 60a and 60b actually comprise only a single dot each, as they provide relatively close aiming points at only one hundred and two hundred yards, respectively. FIG. 1D's aim point field 50 is configured for a rifle and scope system (e.g., 4) which has been “zeroed” (i.e., adjusted to exactly compensate for the drop of the bullet during its flight) at a distance of three hundred yards, as evidenced by the primary horizontal crosshair 52. Thus, a marksman aiming at a closer target must lower his aim point to one of the dots 60a or 60b slightly above the horizontal crosshair 52, as relatively little drop occurs to the bullet in such a relatively short flight.
In FIG. 1D, most of the horizontal rows, e.g. rows 60d, 60e, 60f, 60g, down to row 60n, are numbered to indicate the range in hundreds of yards for an accurate shot using the dots of that particular row. The row 60i has a horizontal mark to indicate a range of one thousand yards. It will be noted that the spacing between each horizontal row 60c, 60d, 60e, 60f, etc., gradually increases as the range becomes longer and longer. This is due to the slowing of the bullet and increase in vertical speed due to the acceleration of gravity during its flight. The alignment and spacing of the horizontal rows nearly compensates for these factors, such that the vertical impact point of the bullet will be more nearly accurate at the selected range. In a similar manner, the generally vertical columns 62a, 62b, 64a, 64b, etc., spread as they extend downwardly to greater and greater ranges. These generally vertical columns are provided as an aiming aid permitting the shooter to compensate for windage, i.e. the lateral drift of a bullet due to any crosswind component. A crosswind will have an ever greater effect upon the path of a bullet with longer and longer range or distance, so the vertical columns spread with greater ranges or distances, with the two inner columns 62a, 64a closest to the central column 54 being spaced to provide correction for a five mile per hour crosswind component, while the next two adjacent columns 62b, 64b providing an estimated correction for a ten mile per hour crosswind component. Long range, high wind aim point estimation is known to the most difficult problem among experienced marksman, even if the wind is relatively steady over the entire flight path of the bullet.
Both of the reticles discussed above represent significant aids for precision shooting over long ranges, such as the ranges depicted in FIG. 1E, (which duplicates the information in FIG. 3-25 of Ref 5). As noted above, FIG. 1E is a trajectory chart taken from a U.S. Gov't publication which illustrates the trajectory and Center of Impact (“COI”) of a selected 7.62×51 (or 7.62 NATO) projectile fired from an M24 SWS rifle for sight adjustment or “zero” settings from 300 meters to 1000 meters. This chart was originally developed as a training aid for military marksmen (e.g., snipers) and illustrates the “zero wind” trajectory for the US M118 7.62 NATO (173gr FMJBT) projectile. The chart is intended to illustrate the arcuate trajectory of the bullet, in flight, and shows the relationship between a “line of sight” and the bullet's trajectory between the shooter's position and a POA or target, for eight different “zero” or sight adjustment ranges, namely, 300M, 400M, 500M, 600M, 700M, 800M, 900M, and 1000M. As illustrated in FIG. 1E, if a shooter is “zeroed” for a target at 300M and shoots a target at 300M, then the highest point of flight in the bullet's trajectory is 6.2 inches and the bullet will strike a target at 400M 14 inches low. This is to be contrasted with a much longer range shot. For example, as illustrated in FIG. 1E, if a shooter is “zeroed” for a target at 900M and shoots a target at 900M, then the highest point of flight in the bullet's trajectory is 96.6 inches (over 8 feet) and the bullet will strike a target at 1000M (or 1.0 KM) 14 inches low. For a target at 1000M the highest point of flight in the bullet's trajectory is 129 inches (almost 11 feet) above the line of sight, and, at these ranges, the bullet's trajectory is clearly well above the line of sight for a significant distance, and the bullet's time of flight (“TOF”) is long enough that the time for the any cross wind to act on the bullet is a more significant factor.
FIG. 1F is another trajectory chart which illustrates the effect of shooting uphill or downhill at a ballistically significant angle above or below horizontal, a practice known as “Angle Firing.” FIG. 1F illustrates the trajectory or path of a projectile 26 aimed from a rifle 4 at a distant, downhill Point of Aim (“POA”), namely target 28. The bullet's path to the target is an arcuate or parabolic trajectory which is mostly above a “Line of Sight” (“LOS”) 29 defined between the rifle 4 and the target 28 and the Line of Sight distance may be measured (e.g., with a laser rangefinder) to provide an “LOS Range”. In the illustrated example, shooter and rifle 4 are above the target 28 by an elevation difference of “Y” (e.g. in yards or meters) and shooting downhill at a resultant “Slope Angle” 27, and the horizontal range or distance “X” covered by the projectile (e.g. in yards or meters) is known to be given by the following equation:X=cos(Slope Angle)×(LOS Range)  (1)The horizontal or “cosine” range X is always less than the LOS Range and so the bullet's ballistic “drop” over the angled trajectory is less than would be for a shot fired across level ground (where X equals LOS range), and the relationship described in eq. 1 is true whether the target 28 is uphill or downhill (as shown) from the shooter. The Slope Angle's ballistic effect must be accounted for when making precise long range shots and many accessories have been developed to help Angle Firing shooters in the field measure a Slope Angle 27 and then compute the cosine range when developing their firing solution.
The above described systems are now in use in scope reticles, but these prior art systems have been discovered to include subtle but significant errors arising from recently observed external ballistic phenomena, and the observed error has been significant (e.g., exceeding one MOA) at ranges well within the operationally significant military or police sniping range limits (e.g., 1000 yards). The prior art systems often require the marksman or shooter to bring a companion (e.g., a coach or spotter) who may be required to bring additional optics for observation and measurement and may also be required to bring along transportable computer-like devices such as a Personal Digital Assistant (“PDA”) or a smart phone (e.g., an iPhone™ or a Blackberry™ programmed with an appropriate software application or “app”) for solving ballistics problems while in the field.
These prior art systems also require the marksman or their companion to engage in too many evaluations and calculations while in the field, and even for experienced long-range shooters, those evaluations and calculations usually take up a significant amount of time. If the marksman is engaged in military or police tactical or sniping operations, lost time when aiming may be extremely critical, (e.g., as noted in Refs 5 and 6).
None of the above cited references or patents, alone or in combination, address the combined atmospheric and ballistic problems identified by the applicant of the present invention or provide an adequately workable and time-efficient way of developing an accurate firing solution, while in the field. Thus, there is an unmet need for a rapid, accurate and effective rifle sight or projectile weapon aiming system and method for more precisely estimating a correct point of aim when shooting or engaging targets at long distances, especially in windy conditions.